1. 5.5 Finding Roots (zeros) by Factoring Remember: MT5 centers around the Algebra of Quadratics and MT6 focuses on the Graphing of Quadratics. Whatever you do in MT5 will be used in MT6. What will we learn in this lesson? How to turn this math statement… x 2 + 8x + 12 = 0 Into this answer… x = -6, -2 Let’s Begin

2. 5.5 Finding Roots (zeros) by Factoring Zero Product Property: If you have a group of numbers or variables that you are multiplying, if any one of them is “0”, then the answer is “0” Just watch. What are the answers? 1. 3 * 5 * 8 * 0 * 7 = ? 2. x * y * 4 * a * 0 = ? Both answers are “0” because you multiplied by zero!

3. 5.5 Finding Roots (zeros) by Factoring Zero Product Property will be used to find two special points on a graph. These points are… Roots (zeros) In this lesson, you will have to find the points Algebraically (no graphing involved)

4. 5.5 Finding Roots (zeros) by Factoring The standard form of a quadratic… x 2 + 5x – 14 = 0 We need to factor this quadratic to find the roots. I will use diamond method… (x )(x ) = 0 -14 5 7 -2 + 7 - 2 If you don’t use diamond method, you may use guess and check, generic rectangle, or factor by grouping. If you need more help with factoring, ask your LF. When in doubt, the Quadratic Formula will always work!

5. 5.5 Finding Roots (zeros) by Factoring Now lets use zero product property… (x + 7 )(x - 2 ) = 0 (x + 7 ) = 0 (x - 2 ) = 0 If either factor becomes “0”, the answer is “0” If x = -7 or x = 2, the answer will be “0” The answer: x = -7, 2 Hint: take the number, change signs

6. 5.5 Finding Roots (zeros) by Factoring Now you try one… x 2 + 9x + 20 = 0 Answer: The answer: x = -5, -4 (x )(x ) = 0 20 9 5 4 + 5 + 4